Texture mapping is used in computer graphics as a way to enhance the visual richness of a three-dimensional (3-D) surface. For example, texture mapping is often used to enhance computer graphics from overly simplified character meshes in game engines, to complex digital models in computer-generated feature films. Seamlessly mapping multiple synthesized and/or real-life textures onto 3-D models for surface decoration, with little visual distortion, can be very difficult and labor-intensive to accomplish by hand, or otherwise. For example, seamlessly mapping a series of real-life photos onto a 3-D model requires alignment of the features of the texture images and the models. Such alignment requires an impractical amount of manual work to put dense constraints along patch boundaries. Additionally, even if boundary continuity is somehow provided, the number of correspondences required to guarantee that each triangle of the original domain has corresponding texture coordinates in a texture image can be arbitrarily large for meshes of high genus, making conventional texture mapping techniques, once again, impractical for a user.